def contract_2e(eri, fcivec, norb, nelec, link_index=None, orbsym=[]):
if not orbsym:
return direct_spin1.contract_2e(eri, fcivec, norb, nelec, link_index)
eri = pyscf.ao2mo.restore(4, eri, norb)
if link_index is None:
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
else:
link_indexa, link_indexb = link_index
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
fcivec = fcivec.reshape(na,nb)
ci1 = numpy.empty_like(fcivec)
eri, link_indexa, dimirrep = reorder4irrep(eri, norb, link_indexa, orbsym)
link_indexb = reorder4irrep(eri, norb, link_indexb, orbsym)[1]
dimirrep = numpy.array(dimirrep, dtype=numpy.int32)
libfci.FCIcontract_2e_spin1_symm(eri.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p),
dimirrep.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(dimirrep)))
return ci1
def contract_1e(f1e, fcivec, norb, nelec, link_index=None):
assert(fcivec.flags.c_contiguous)
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
if link_index is None:
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
else:
link_indexa, link_indexb = link_index
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
ci1 = numpy.zeros((na,nb))
f1e_tril = pyscf.lib.pack_tril(f1e[0])
libfci.FCIcontract_a_1e(f1e_tril.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p))
f1e_tril = pyscf.lib.pack_tril(f1e[1])
libfci.FCIcontract_b_1e(f1e_tril.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p))
return ci1
def pspace(h1e, eri, norb, nelec, hdiag, np=400):
neleca, nelecb = direct_spin1._unpack_nelec(nelec)
h1e_a = numpy.ascontiguousarray(h1e[0])
h1e_b = numpy.ascontiguousarray(h1e[1])
g2e_aa = ao2mo.restore(1, eri[0], norb)
g2e_ab = ao2mo.restore(1, eri[1], norb)
g2e_bb = ao2mo.restore(1, eri[2], norb)
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
nb = link_indexb.shape[0]
addr = numpy.argsort(hdiag)[:np]
addra = addr // nb
addrb = addr % nb
stra = numpy.array([cistring.addr2str(norb,neleca,ia) for ia in addra],
dtype=numpy.long)
strb = numpy.array([cistring.addr2str(norb,nelecb,ib) for ib in addrb],
dtype=numpy.long)
np = len(addr)
h0 = numpy.zeros((np,np))
libfci.FCIpspace_h0tril_uhf(h0.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
g2e_aa.ctypes.data_as(ctypes.c_void_p),
g2e_ab.ctypes.data_as(ctypes.c_void_p),
g2e_bb.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i,i] = hdiag[addr[i]]
h0 = lib.hermi_triu(h0)
return addr, h0
def contract_2e(eri, fcivec, norb, nelec, link_index=None):
assert(fcivec.flags.c_contiguous)
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
g2e_aa = pyscf.ao2mo.restore(4, eri[0], norb)
g2e_ab = pyscf.ao2mo.restore(4, eri[1], norb)
g2e_bb = pyscf.ao2mo.restore(4, eri[2], norb)
if link_index is None:
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
else:
link_indexa, link_indexb = link_index
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
fcivec = fcivec.reshape(na,nb)
ci1 = numpy.empty_like(fcivec)
libfci.FCIcontract_uhf2e(g2e_aa.ctypes.data_as(ctypes.c_void_p),
g2e_ab.ctypes.data_as(ctypes.c_void_p),
g2e_bb.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p))
return ci1
def contract_2e(eri, fcivec, norb, nelec, link_index=None):
eri = pyscf.ao2mo.restore(4, eri, norb)
if link_index is None:
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
else:
link_indexa, link_indexb = link_index
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
fcivec = fcivec.reshape(na,nb)
ci1 = numpy.empty_like(fcivec)
libfci.FCIcontract_2e_spin1(eri.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p))
return ci1
def _unpack(norb, nelec, link_index, spin=None):
if link_index is None:
neleca, nelecb = _unpack_nelec(nelec, spin)
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
return link_indexa, link_indexb
else:
return link_index
def _unpack(norb, nelec, link_index, spin=None):
if link_index is None:
neleca, nelecb = _unpack_nelec(nelec, spin)
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
return link_indexa, link_indexb
else:
return link_index
def kernel_ms1(fci, h1e, eri, norb, nelec, ci0=None, **kwargs):
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
nelec = (neleca, nelecb)
else:
neleca, nelecb = nelec
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
na = link_indexa.shape[0]
nb = link_indexb.shape[0]
hdiag = fci.make_hdiag(h1e, eri, norb, nelec)
addr, h0 = fci.pspace(h1e, eri, norb, nelec, hdiag, fci.pspace_size)
pw, pv = scipy.linalg.eigh(h0)
# The degenerated wfn can break symmetry. The davidson iteration with proper
# initial guess doesn't have this issue
if not fci.davidson_only:
if len(pw) == na*nb:
if na*nb == 1:
return pw[0], pv[:,0]
elif fci.nroots > 1:
civec = numpy.empty((fci.nroots,na*nb))
civec[:,addr] = pv[:,:fci.nroots].T
return pw[:fci.nroots], civec.reshape(fci.nroots,na,nb)
elif abs(pw[0]-pw[1]) > 1e-12:
civec = numpy.empty((na*nb))
civec[addr] = pv[:,0]
return pw[0], civec.reshape(na,nb)
precond = fci.make_precond(hdiag, pw, pv, addr)
h2e = fci.absorb_h1e(h1e, eri, norb, nelec, .5)
def hop(c):
hc = fci.contract_2e(h2e, c, norb, nelec, (link_indexa,link_indexb))
return hc.ravel()
if ci0 is None:
if hasattr(fci, 'get_init_guess'):
ci0 = fci.get_init_guess(norb, nelec, fci.nroots, hdiag)
else:
ci0 = []
for i in range(fci.nroots):
x = numpy.zeros(na*nb)
x[addr[i]] = 1
ci0.append(x)
else:
if isinstance(ci0, numpy.ndarray) and ci0.size == na*nb:
ci0 = [ci0.ravel()]
else:
ci0 = [x.ravel() for x in ci0]
#e, c = pyscf.lib.davidson(hop, ci0, precond, tol=fci.conv_tol, lindep=fci.lindep)
e, c = fci.eig(hop, ci0, precond, **kwargs)
if fci.nroots > 1:
return e, [ci.reshape(na,nb) for ci in c]
else:
return e, c.reshape(na,nb)
def gen_linkstr(self, norb, nelec, tril=True, spin=None):
if spin is None:
spin = self.spin
neleca, nelecb = _unpack_nelec(nelec, spin)
if tril:
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
else:
link_indexa = cistring.gen_linkstr_index(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index(range(norb), nelecb)
return link_indexa, link_indexb
def gen_linkstr(self, norb, nelec, tril=True, spin=None):
if spin is None:
spin = self.spin
neleca, nelecb = _unpack_nelec(nelec, spin)
if tril:
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
else:
link_indexa = cistring.gen_linkstr_index(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index(range(norb), nelecb)
return link_indexa, link_indexb
def _unpack(norb, nelec, link_index):
if link_index is None:
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
return link_indexa, link_indexb
else:
return link_index
def _unpack(norb, nelec, link_index):
if link_index is None:
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
return link_indexa, link_indexb
else:
return link_index
def contract_2e(eri, fcivec, norb, nelec, link_index=None):
r'''Contract the 2-electron Hamiltonian with a FCI vector to get a new FCI
vector.
Note the input arg eri is NOT the 2e hamiltonian matrix, the 2e hamiltonian is
.. math::
h2e &= eri_{pq,rs} p^+ q r^+ s \\
&= (pq|rs) p^+ r^+ s q - (pq|rs) \delta_{qr} p^+ s
So eri is defined as
.. math::
eri_{pq,rs} = (pq|rs) - (1/Nelec) \sum_q (pq|qs)
to restore the symmetry between pq and rs,
.. math::
eri_{pq,rs} = (pq|rs) - (.5/Nelec) [\sum_q (pq|qs) + \sum_p (pq|rp)]
Please refer to the treatment in :func:`direct_spin1.absorb_h1e`
'''
assert(fcivec.flags.c_contiguous)
eri = pyscf.ao2mo.restore(4, eri, norb)
if link_index is None:
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
else:
link_indexa, link_indexb = link_index
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
fcivec = fcivec.reshape(na,nb)
ci1 = numpy.empty_like(fcivec)
libfci.FCIcontract_2e_spin1(eri.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p))
return ci1
def test_linkstr_index(self):
idx1 = cistring.gen_linkstr_index_o0(range(4), 2)
idx2 = cistring.gen_linkstr_index(range(4), 2)
idx23 = numpy.array([[0, 0, 3, 1],
[3, 3, 3, 1],
[1, 0, 4, 1],
[2, 0, 5, 1],
[1, 3, 0, 1],
[2, 3, 1, 1],])
self.assertTrue(numpy.all(idx1[:,:,2:] == idx2[:,:,2:]))
self.assertTrue(numpy.all(idx23 == idx2[3]))
idx1 = cistring.gen_linkstr_index(range(7), 3)
idx2 = cistring.reform_linkstr_index(idx1)
idx3 = cistring.gen_linkstr_index_trilidx(range(7), 3)
idx3[:,:,1] = 0
self.assertTrue(numpy.all(idx2 == idx3))
tab1 = cistring.gen_cre_str_index_o0(range(8), 4)
tab2 = cistring.gen_cre_str_index_o1(range(8), 4)
self.assertAlmostEqual(abs(tab1 - tab2).max(), 0, 12)
tab1 = cistring.gen_des_str_index_o0(range(8), 4)
tab2 = cistring.gen_des_str_index_o1(range(8), 4)
self.assertAlmostEqual(abs(tab1 - tab2).max(), 0, 12)
tab1 = cistring.gen_linkstr_index_o0(range(8), 4)
tab2 = cistring.gen_linkstr_index(range(8), 4)
self.assertAlmostEqual(abs(tab1 - tab2).sum(), 0, 12)
tab3 = cistring.gen_linkstr_index_o1(range(8), 4)
self.assertAlmostEqual(abs(tab1 - tab3).sum(), 0, 12)
def test_linkstr_index(self):
idx1 = cistring.gen_linkstr_index_o0(range(4), 2)
idx2 = cistring.gen_linkstr_index(range(4), 2)
idx23 = numpy.array([
[0, 0, 3, 1],
[3, 3, 3, 1],
[1, 0, 4, 1],
[2, 0, 5, 1],
[1, 3, 0, 1],
[2, 3, 1, 1],
])
self.assertTrue(numpy.all(idx1[:, :, 2:] == idx2[:, :, 2:]))
self.assertTrue(numpy.all(idx23 == idx2[3]))
idx1 = cistring.gen_linkstr_index(range(7), 3)
idx2 = cistring.reform_linkstr_index(idx1)
idx3 = cistring.gen_linkstr_index_trilidx(range(7), 3)
idx3[:, :, 1] = 0
self.assertTrue(numpy.all(idx2 == idx3))
tab1 = cistring.gen_cre_str_index_o0(range(8), 4)
tab2 = cistring.gen_cre_str_index_o1(range(8), 4)
self.assertAlmostEqual(abs(tab1 - tab2).max(), 0, 12)
tab1 = cistring.gen_des_str_index_o0(range(8), 4)
tab2 = cistring.gen_des_str_index_o1(range(8), 4)
self.assertAlmostEqual(abs(tab1 - tab2).max(), 0, 12)
tab1 = cistring.gen_linkstr_index_o0(range(8), 4)
tab2 = cistring.gen_linkstr_index(range(8), 4)
self.assertAlmostEqual(abs(tab1 - tab2).sum(), 0, 12)
tab3 = cistring.gen_linkstr_index_o1(range(8), 4)
self.assertAlmostEqual(abs(tab1 - tab3).sum(), 0, 12)
def contract_2e(eri, fcivec, norb, nelec, link_index=None, orbsym=[]):
assert(fcivec.flags.c_contiguous)
if not list(orbsym):
return direct_spin0.contract_2e(eri, fcivec, norb, nelec, link_index)
eri = pyscf.ao2mo.restore(4, eri, norb)
if link_index is None:
if isinstance(nelec, (int, numpy.integer)):
neleca = nelec//2
else:
neleca, nelecb = nelec
assert(neleca == nelecb)
link_index = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
na,nlink,_ = link_index.shape
ci1 = numpy.empty((na,na))
eri, link_index, dimirrep = \
direct_spin1_symm.reorder4irrep(eri, norb, link_index, orbsym)
dimirrep = numpy.array(dimirrep, dtype=numpy.int32)
libfci.FCIcontract_2e_spin0_symm(eri.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(na),
ctypes.c_int(nlink),
link_index.ctypes.data_as(ctypes.c_void_p),
dimirrep.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(len(dimirrep)))
return pyscf.lib.transpose_sum(ci1, inplace=True)
def kernel_ms0(fci, h1e, eri, norb, nelec, ci0=None, **kwargs):
if isinstance(nelec, (int, numpy.integer)):
neleca = nelec//2
else:
neleca, nelecb = nelec
assert(neleca == nelecb)
h1e = numpy.ascontiguousarray(h1e)
eri = numpy.ascontiguousarray(eri)
link_index = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
na = link_index.shape[0]
hdiag = fci.make_hdiag(h1e, eri, norb, nelec)
addr, h0 = fci.pspace(h1e, eri, norb, nelec, hdiag, fci.pspace_size)
pw, pv = scipy.linalg.eigh(h0)
# The degenerated wfn can break symmetry. The davidson iteration with proper
# initial guess doesn't have this issue
if not fci.davidson_only:
if len(addr) == 1:
return pw, pv
elif len(addr) == na*na:
if fci.nroots > 1:
ci0 = numpy.empty((fci.nroots,na*na))
ci0[:,addr] = pv[:,:fci.nroots].T
return pw[:fci.nroots], ci0.reshape(fci.nroots,na,na)
elif abs(pw[0]-pw[1]) > 1e-12:
ci0 = numpy.empty((na*na))
ci0[addr] = pv[:,0]
ci0 = ci0.reshape(na,na)
ci0 = pyscf.lib.transpose_sum(ci0, inplace=True) * .5
# direct diagonalization may lead to triplet ground state
##TODO: optimize initial guess. Using pspace vector as initial guess may have
## spin problems. The 'ground state' of psapce vector may have different spin
## state to the true ground state.
if numpy.allclose(numpy.linalg.norm(ci0), 1):
return pw[0], ci0.reshape(na,na)
precond = fci.make_precond(hdiag, pw, pv, addr)
h2e = fci.absorb_h1e(h1e, eri, norb, nelec, .5)
def hop(c):
hc = fci.contract_2e(h2e, c, norb, nelec, link_index)
return hc.ravel()
#TODO: check spin of initial guess
if ci0 is None:
# we need better initial guess
ci0 = numpy.zeros(na*na)
#ci0[addr] = pv[:,0]
ci0[0] = 1
else:
# symmetrize the initial guess, otherwise got strange numerical noise after
# couple of davidson iterations
# ci0 = pyscf.lib.transpose_sum(ci0.reshape(na,na)).ravel()*.5
ci0 = ci0.ravel()
#e, c = pyscf.lib.davidson(hop, ci0, precond, tol=fci.conv_tol, lindep=fci.lindep)
e, c = fci.eig(hop, ci0, precond, **kwargs)
return e, c.reshape(na,na)
def _unpack(norb, nelec, link_index):
if link_index is None:
if isinstance(nelec, (int, numpy.number)):
neleca = nelec // 2
else:
neleca, nelecb = nelec
assert (neleca == nelecb)
return cistring.gen_linkstr_index_trilidx(range(norb), neleca)
else:
return link_index
def _unpack(norb, nelec, link_index):
if link_index is None:
if isinstance(nelec, (int, numpy.number)):
neleca = nelec//2
else:
neleca, nelecb = nelec
assert(neleca == nelecb)
return cistring.gen_linkstr_index_trilidx(range(norb), neleca)
else:
return link_index
def gen_linkstr(self, norb, nelec, tril=True, spin=None):
if isinstance(nelec, (int, numpy.number)):
neleca = nelec//2
else:
neleca, nelecb = nelec
assert(neleca == nelecb)
if tril:
link_index = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
else:
link_index = cistring.gen_linkstr_index(range(norb), neleca)
return link_index
def gen_linkstr(self, norb, nelec, tril=True, spin=None):
if isinstance(nelec, (int, numpy.number)):
neleca = nelec//2
else:
neleca, nelecb = nelec
assert(neleca == nelecb)
if tril:
link_index = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
else:
link_index = cistring.gen_linkstr_index(range(norb), neleca)
return link_index
def pspace(h1e, eri, norb, nelec, hdiag=None, np=400):
neleca, nelecb = direct_spin1._unpack_nelec(nelec)
h1e_a = numpy.ascontiguousarray(h1e[0])
h1e_b = numpy.ascontiguousarray(h1e[1])
g2e_aa = ao2mo.restore(1, eri[0], norb)
g2e_ab = ao2mo.restore(1, eri[1], norb)
g2e_bb = ao2mo.restore(1, eri[2], norb)
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
nb = link_indexb.shape[0]
if hdiag is None:
hdiag = make_hdiag(h1e, eri, norb, nelec)
if hdiag.size < np:
addr = numpy.arange(hdiag.size)
else:
try:
addr = numpy.argpartition(hdiag, np - 1)[:np]
except AttributeError:
addr = numpy.argsort(hdiag)[:np]
addra = addr // nb
addrb = addr % nb
stra = numpy.array([cistring.addr2str(norb, neleca, ia) for ia in addra],
dtype=numpy.long)
strb = numpy.array([cistring.addr2str(norb, nelecb, ib) for ib in addrb],
dtype=numpy.long)
np = len(addr)
h0 = numpy.zeros((np, np))
libfci.FCIpspace_h0tril_uhf(h0.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
g2e_aa.ctypes.data_as(ctypes.c_void_p),
g2e_ab.ctypes.data_as(ctypes.c_void_p),
g2e_bb.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i, i] = hdiag[addr[i]]
h0 = lib.hermi_triu(h0)
return addr, h0
def pspace(h1e, eri, norb, nelec, hdiag, np=400):
if isinstance(nelec, (int, numpy.number)):
nelecb = nelec // 2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
h1e_a = numpy.ascontiguousarray(h1e[0])
h1e_b = numpy.ascontiguousarray(h1e[1])
g2e_aa = pyscf.ao2mo.restore(1, eri[0], norb)
g2e_ab = pyscf.ao2mo.restore(1, eri[1], norb)
g2e_bb = pyscf.ao2mo.restore(1, eri[2], norb)
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
nb = link_indexb.shape[0]
addr = numpy.argsort(hdiag)[:np]
addra = addr // nb
addrb = addr % nb
stra = numpy.array([cistring.addr2str(norb, neleca, ia) for ia in addra],
dtype=numpy.long)
strb = numpy.array([cistring.addr2str(norb, nelecb, ib) for ib in addrb],
dtype=numpy.long)
np = len(addr)
h0 = numpy.zeros((np, np))
libfci.FCIpspace_h0tril_uhf(h0.ctypes.data_as(ctypes.c_void_p),
h1e_a.ctypes.data_as(ctypes.c_void_p),
h1e_b.ctypes.data_as(ctypes.c_void_p),
g2e_aa.ctypes.data_as(ctypes.c_void_p),
g2e_ab.ctypes.data_as(ctypes.c_void_p),
g2e_bb.ctypes.data_as(ctypes.c_void_p),
stra.ctypes.data_as(ctypes.c_void_p),
strb.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(np))
for i in range(np):
h0[i, i] = hdiag[addr[i]]
h0 = pyscf.lib.hermi_triu(h0)
return addr, h0
def contract_1e(f1e, fcivec, norb, nelec, link_index=None):
'''Contract the 1-electron Hamiltonian with a FCI vector to get a new FCI
vector.
'''
if link_index is None:
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
else:
neleca, nelecb = nelec
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
else:
link_indexa, link_indexb = link_index
na, nlinka = link_indexa.shape[:2]
nb, nlinkb = link_indexb.shape[:2]
f1e_tril = pyscf.lib.pack_tril(f1e)
ci1 = numpy.zeros((na,nb))
libfci.FCIcontract_a_1e(f1e_tril.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p))
libfci.FCIcontract_b_1e(f1e_tril.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na), ctypes.c_int(nb),
ctypes.c_int(nlinka), ctypes.c_int(nlinkb),
link_indexa.ctypes.data_as(ctypes.c_void_p),
link_indexb.ctypes.data_as(ctypes.c_void_p))
return ci1
def test_linkstr_index(self):
idx1 = cistring.gen_linkstr_index_o0(range(4), 2)
idx2 = cistring.gen_linkstr_index(range(4), 2)
idx23 = numpy.array([[0, 0, 3, 1],
[3, 3, 3, 1],
[1, 0, 4, 1],
[2, 0, 5, 1],
[1, 3, 0, 1],
[2, 3, 1, 1],])
self.assertTrue(numpy.all(idx1[:,:,2:] == idx2[:,:,2:]))
self.assertTrue(numpy.all(idx23 == idx2[3]))
idx1 = cistring.gen_linkstr_index(range(7), 3)
idx2 = cistring.reform_linkstr_index(idx1)
idx3 = cistring.gen_linkstr_index_trilidx(range(7), 3)
idx3[:,:,1] = 0
self.assertTrue(numpy.all(idx2 == idx3))
def test_linkstr_index(self):
idx1 = cistring.gen_linkstr_index_o0(range(4), 2)
idx2 = cistring.gen_linkstr_index(range(4), 2)
idx23 = numpy.array([[0, 0, 3, 1],
[3, 3, 3, 1],
[1, 0, 4, 1],
[2, 0, 5, 1],
[1, 3, 0, 1],
[2, 3, 1, 1],])
self.assertTrue(numpy.all(idx1[:,:,2:] == idx2[:,:,2:]))
self.assertTrue(numpy.all(idx23 == idx2[3]))
idx1 = cistring.gen_linkstr_index(range(7), 3)
idx2 = cistring.reform_linkstr_index(idx1)
idx3 = cistring.gen_linkstr_index_trilidx(range(7), 3)
idx3[:,:,1] = 0
self.assertTrue(numpy.all(idx2 == idx3))
def contract_1e(f1e, fcivec, norb, nelec, link_index=None):
if link_index is None:
if isinstance(nelec, (int, numpy.integer)):
neleca = nelec//2
else:
neleca, nelecb = nelec
assert(neleca == nelecb)
link_index = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
na,nlink,_ = link_index.shape
ci1 = numpy.empty((na,na))
f1e_tril = pyscf.lib.pack_tril(f1e)
libfci.FCIcontract_1e_spin0(f1e_tril.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb), ctypes.c_int(na),
ctypes.c_int(nlink),
link_index.ctypes.data_as(ctypes.c_void_p))
# no *.5 because FCIcontract_2e_spin0 only compute half of the contraction
return pyscf.lib.transpose_sum(ci1, inplace=True)
def contract_2e(eri, fcivec, norb, nelec, link_index=None):
assert fcivec.flags.c_contiguous
eri = pyscf.ao2mo.restore(4, eri, norb)
if link_index is None:
if isinstance(nelec, (int, numpy.integer)):
neleca = nelec // 2
else:
neleca, nelecb = nelec
assert neleca == nelecb
link_index = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
na, nlink, _ = link_index.shape
ci1 = numpy.empty((na, na))
libfci.FCIcontract_2e_spin0(
eri.ctypes.data_as(ctypes.c_void_p),
fcivec.ctypes.data_as(ctypes.c_void_p),
ci1.ctypes.data_as(ctypes.c_void_p),
ctypes.c_int(norb),
ctypes.c_int(na),
ctypes.c_int(nlink),
link_index.ctypes.data_as(ctypes.c_void_p),
)
# no *.5 because FCIcontract_2e_spin0 only compute half of the contraction
return pyscf.lib.transpose_sum(ci1, inplace=True)
def kernel_ms0(fci, h1e, eri, norb, nelec, ci0=None, **kwargs):
if isinstance(nelec, (int, numpy.integer)):
neleca = nelec//2
else:
neleca, nelecb = nelec
assert(neleca == nelecb)
h1e = numpy.ascontiguousarray(h1e)
eri = numpy.ascontiguousarray(eri)
link_index = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
na = link_index.shape[0]
hdiag = fci.make_hdiag(h1e, eri, norb, nelec)
addr, h0 = fci.pspace(h1e, eri, norb, nelec, hdiag, fci.pspace_size)
pw, pv = scipy.linalg.eigh(h0)
# The degenerated wfn can break symmetry. The davidson iteration with proper
# initial guess doesn't have this issue
if not fci.davidson_only:
if len(addr) == na*na:
if na*na == 1:
return pw[0], pv[:,0]
elif fci.nroots > 1:
civec = numpy.empty((fci.nroots,na*na))
civec[:,addr] = pv[:,:fci.nroots].T
civec = civec.reshape(fci.nroots,na,na)
try:
return pw[:fci.nroots], [_check_(ci) for ci in civec]
except ValueError:
pass
elif abs(pw[0]-pw[1]) > 1e-12:
civec = numpy.empty((na*na))
civec[addr] = pv[:,0]
civec = civec.reshape(na,na)
civec = pyscf.lib.transpose_sum(civec) * .5
# direct diagonalization may lead to triplet ground state
##TODO: optimize initial guess. Using pspace vector as initial guess may have
## spin problems. The 'ground state' of psapce vector may have different spin
## state to the true ground state.
try:
return pw[0], _check_(civec.reshape(na,na))
except ValueError:
pass
precond = fci.make_precond(hdiag, pw, pv, addr)
h2e = fci.absorb_h1e(h1e, eri, norb, nelec, .5)
def hop(c):
hc = fci.contract_2e(h2e, c, norb, nelec, link_index)
return hc.ravel()
#TODO: check spin of initial guess
if ci0 is None:
if hasattr(fci, 'get_init_guess'):
ci0 = fci.get_init_guess(norb, nelec, fci.nroots, hdiag)
else:
ci0 = []
for i in range(fci.nroots):
x = numpy.zeros(na,na)
if addr[i] == 0:
x[0,0] = 1
else:
addra = addr[i] // na
addrb = addr[i] % na
x[addra,addrb] = x[addrb,addra] = numpy.sqrt(.5)
ci0.append(x.ravel())
else:
if isinstance(ci0, numpy.ndarray) and ci0.size == na*na:
ci0 = [ci0.ravel()]
else:
ci0 = [x.ravel() for x in ci0]
#e, c = pyscf.lib.davidson(hop, ci0, precond, tol=fci.conv_tol, lindep=fci.lindep)
e, c = fci.eig(hop, ci0, precond, **kwargs)
if fci.nroots > 1:
return e, [_check_(ci.reshape(na,na)) for ci in c]
else:
return e, _check_(c.reshape(na,na))
def kernel_ms1(fci, h1e, eri, norb, nelec, ci0=None,
tol=None, lindep=None, max_cycle=None, max_space=None,
nroots=None, davidson_only=None, pspace_size=None,
max_memory=None, verbose=None, **kwargs):
if nroots is None: nroots = fci.nroots
if davidson_only is None: davidson_only = fci.davidson_only
if pspace_size is None: pspace_size = fci.pspace_size
if isinstance(nelec, (int, numpy.integer)):
nelecb = nelec//2
neleca = nelec - nelecb
nelec = (neleca, nelecb)
else:
neleca, nelecb = nelec
link_indexa = cistring.gen_linkstr_index_trilidx(range(norb), neleca)
link_indexb = cistring.gen_linkstr_index_trilidx(range(norb), nelecb)
na = link_indexa.shape[0]
nb = link_indexb.shape[0]
hdiag = fci.make_hdiag(h1e, eri, norb, nelec)
if pspace_size > 0:
addr, h0 = fci.pspace(h1e, eri, norb, nelec, hdiag, pspace_size)
pw, pv = scipy.linalg.eigh(h0)
else:
pw = pv = addr = None
if pspace_size >= na*nb and ci0 is not None and not davidson_only:
# The degenerated wfn can break symmetry. The davidson iteration with proper
# initial guess doesn't have this issue
if na*nb == 1:
return pw[0], pv[:,0]
elif nroots > 1:
civec = numpy.empty((nroots,na*nb))
civec[:,addr] = pv[:,:nroots].T
return pw[:nroots], civec.reshape(nroots,na,nb)
elif abs(pw[0]-pw[1]) > 1e-12:
civec = numpy.empty((na*nb))
civec[addr] = pv[:,0]
return pw[0], civec.reshape(na,nb)
precond = fci.make_precond(hdiag, pw, pv, addr)
h2e = fci.absorb_h1e(h1e, eri, norb, nelec, .5)
def hop(c):
hc = fci.contract_2e(h2e, c, norb, nelec, (link_indexa,link_indexb))
return hc.ravel()
if ci0 is None:
if hasattr(fci, 'get_init_guess'):
ci0 = fci.get_init_guess(norb, nelec, nroots, hdiag)
else:
ci0 = []
for i in range(nroots):
x = numpy.zeros(na*nb)
x[addr[i]] = 1
ci0.append(x)
else:
if isinstance(ci0, numpy.ndarray) and ci0.size == na*nb:
ci0 = [ci0.ravel()]
else:
ci0 = [x.ravel() for x in ci0]
if tol is None: tol = fci.conv_tol
if lindep is None: lindep = fci.lindep
if max_cycle is None: max_cycle = fci.max_cycle
if max_space is None: max_space = fci.max_space
if max_memory is None: max_memory = fci.max_memory
if verbose is None: verbose = pyscf.lib.logger.Logger(fci.stdout, fci.verbose)
#e, c = pyscf.lib.davidson(hop, ci0, precond, tol=fci.conv_tol, lindep=fci.lindep)
e, c = fci.eig(hop, ci0, precond, tol=tol, lindep=lindep,
max_cycle=max_cycle, max_space=max_space, nroots=nroots,
max_memory=max_memory, verbose=verbose, **kwargs)
if nroots > 1:
return e, [ci.reshape(na,nb) for ci in c]
else:
return e, c.reshape(na,nb)